论文标题
神经密度估计的量子自适应傅立叶特征
Quantum Adaptive Fourier Features for Neural Density Estimation
论文作者
论文摘要
密度估计是统计和机器学习应用中的基本任务。内核密度估计是低维度非参数密度估计的强大工具。但是，其性能在更高的维度上很差。此外，其预测复杂性量表与更多的训练数据点线性线性。本文提出了一种神经密度估计的方法，可以将其视为一种核密度估计，但没有高预测计算复杂性。该方法基于密度矩阵，量子力学中使用的形式主义和适应性傅立叶特征。该方法可以在没有优化的情况下进行训练，但也可以与深度学习体系结构进行整合，并使用梯度下降进行训练。因此，它可以看作是神经密度估计方法的一种形式。该方法在不同的合成和实际数据集中进行了评估，其性能与最新的神经密度估计方法相比，获得了竞争结果。
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher dimensions. Moreover, its prediction complexity scale linearly with more training data points. This paper presents a method for neural density estimation that can be seen as a type of kernel density estimation, but without the high prediction computational complexity. The method is based on density matrices, a formalism used in quantum mechanics, and adaptive Fourier features. The method can be trained without optimization, but it could be also integrated with deep learning architectures and trained using gradient descent. Thus, it could be seen as a form of neural density estimation method. The method was evaluated in different synthetic and real datasets, and its performance compared against state-of-the-art neural density estimation methods, obtaining competitive results.
